Discrete Time Asset Pricing Models In Applied Stochastic Finance

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Discrete-time Asset Pricing Models in Applied Stochastic Finance

P. C. G. Vassiliou
Discrete time Asset Pricing Models in Applied Stochastic Finance Book PDF

Author : P. C. G. Vassiliou
Publisher : John Wiley & Sons
Page : 296 pages
File Size : 41,7 Mb
Release : 2013-03-01
Category : Mathematics
ISBN : 9781118618660

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Discrete-time Asset Pricing Models in Applied Stochastic Finance by P. C. G. Vassiliou Pdf

Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financial instruments and the fundamental principles of financial modeling and arbitrage valuation of derivatives. Next, we use the discrete-time binomial model to introduce all relevant concepts. The mathematical simplicity of the binomial model also provides us with the opportunity to introduce and discuss in depth concepts such as conditional expectations and martingales in discrete time. However, we do not expand beyond the needs of the stochastic finance framework. Numerous examples, each highlighted and isolated from the text for easy reference and identification, are included. The book concludes with the use of the binomial model to introduce interest rate models and the use of the Markov chain model to introduce credit risk. This volume is designed in such a way that, among other uses, makes it useful as an undergraduate course.

Continuous-time Asset Pricing Models in Applied Stochastic Finance

P. C. G. Vassiliou
Continuous time Asset Pricing Models in Applied Stochastic Finance Book PDF

Author : P. C. G. Vassiliou
Publisher : Wiley-ISTE
Page : 0 pages
File Size : 49,5 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 1848211597

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Continuous-time Asset Pricing Models in Applied Stochastic Finance by P. C. G. Vassiliou Pdf

Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. In Volume 2 we study continuous time models by presenting the necessary material from continuous martingales, measure theory and stochastic differential equations as models for various assets, such as the Wiener process, Brownian motion, etc. We then build, with many examples and intuitive explanations, the necessary stochastic analysis background i.e. Itô’s lemma, stochastic integration, Girsanovís theorem, etc. The book then guides the reader into the pricing of vanilla options in continuous time i.e. the continuous time models of Black and Scholes, followed by interest rate models and the models of Heath-Jarrow-Morton and the forward Libor model. The final part of the book presents the pricing of credit derivatives.

Asset Pricing

T. Kariya,Regina Liu
Asset Pricing Book PDF

Author : T. Kariya,Regina Liu
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 42,9 Mb
Release : 2011-06-27
Category : Business & Economics
ISBN : 9781441992307

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Asset Pricing by T. Kariya,Regina Liu Pdf

1. Main Goals The theory of asset pricing has grown markedly more sophisticated in the last two decades, with the application of powerful mathematical tools such as probability theory, stochastic processes and numerical analysis. The main goal of this book is to provide a systematic exposition, with practical appli cations, of the no-arbitrage theory for asset pricing in financial engineering in the framework of a discrete time approach. The book should also serve well as a textbook on financial asset pricing. It should be accessible to a broad audi ence, in particular to practitioners in financial and related industries, as well as to students in MBA or graduate/advanced undergraduate programs in finance, financial engineering, financial econometrics, or financial information science. The no-arbitrage asset pricing theory is based on the simple and well ac cepted principle that financial asset prices are instantly adjusted at each mo ment in time in order not to allow an arbitrage opportunity. Here an arbitrage opportunity is an opportunity to have a portfolio of value aat an initial time lead to a positive terminal value with probability 1 (equivalently, at no risk), with money neither added nor subtracted from the portfolio in rebalancing dur ing the investment period. It is necessary for a portfolio of valueato include a short-sell position as well as a long-buy position of some assets.

Stochastic Methods in Asset Pricing

Andrew Lyasoff
Stochastic Methods in Asset Pricing Book PDF

Author : Andrew Lyasoff
Publisher : MIT Press
Page : 632 pages
File Size : 54,8 Mb
Release : 2017-08-25
Category : Business & Economics
ISBN : 9780262036559

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Stochastic Methods in Asset Pricing by Andrew Lyasoff Pdf

A comprehensive overview of the theory of stochastic processes and its connections to asset pricing, accompanied by some concrete applications. This book presents a self-contained, comprehensive, and yet concise and condensed overview of the theory and methods of probability, integration, stochastic processes, optimal control, and their connections to the principles of asset pricing. The book is broader in scope than other introductory-level graduate texts on the subject, requires fewer prerequisites, and covers the relevant material at greater depth, mainly without rigorous technical proofs. The book brings to an introductory level certain concepts and topics that are usually found in advanced research monographs on stochastic processes and asset pricing, and it attempts to establish greater clarity on the connections between these two fields. The book begins with measure-theoretic probability and integration, and then develops the classical tools of stochastic calculus, including stochastic calculus with jumps and Lévy processes. For asset pricing, the book begins with a brief overview of risk preferences and general equilibrium in incomplete finite endowment economies, followed by the classical asset pricing setup in continuous time. The goal is to present a coherent single overview. For example, the text introduces discrete-time martingales as a consequence of market equilibrium considerations and connects them to the stochastic discount factors before offering a general definition. It covers concrete option pricing models (including stochastic volatility, exchange options, and the exercise of American options), Merton's investment–consumption problem, and several other applications. The book includes more than 450 exercises (with detailed hints). Appendixes cover analysis and topology and computer code related to the practical applications discussed in the text.

Stochastic Finance

Nicolas Privault
Stochastic Finance Book PDF

Author : Nicolas Privault
Publisher : CRC Press
Page : 444 pages
File Size : 54,6 Mb
Release : 2013-12-20
Category : Business & Economics
ISBN : 9781466594029

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Stochastic Finance by Nicolas Privault Pdf

Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading. With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.

Lectures on Financial Mathematics

Greg Anderson,Alec Kercheval
Lectures on Financial Mathematics Book PDF

Author : Greg Anderson,Alec Kercheval
Publisher : Springer Nature
Page : 51 pages
File Size : 41,7 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031023996

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Lectures on Financial Mathematics by Greg Anderson,Alec Kercheval Pdf

This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage", the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged to work through the exercises throughout the book. The intended audience is students and other readers who have an undergraduate background in mathematics, including exposure to linear algebra, some advanced calculus, and basic probability. The book has been used in earlier forms with students in the MS program in Financial Mathematics at Florida State University, and is a suitable text for students at that level. Students who seek a second look at these topics may also find this book useful. Table of Contents: Overture: Single-Period Models / The General Discrete Model / The Fundamental Theorems of Asset Pricing / Forwards and Futures / Incomplete Markets

Asset Pricing in Discrete Time

Ser-Huang Poon,Richard Stapleton
Asset Pricing in Discrete Time Book PDF

Author : Ser-Huang Poon,Richard Stapleton
Publisher : Oxford University Press on Demand
Page : 153 pages
File Size : 46,9 Mb
Release : 2005-01-13
Category : Business & Economics
ISBN : 9780199271443

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Asset Pricing in Discrete Time by Ser-Huang Poon,Richard Stapleton Pdf

Relying on the existence, in a complete market, of a pricing kernel, this book covers the pricing of assets, derivatives, and bonds in a discrete time, complete markets framework. It is primarily aimed at advanced Masters and PhD students in finance.-- Covers asset pricing in a single period model, deriving a simple complete market pricing model and using Stein's lemma to derive a version of the Capital Asset Pricing Model.-- Looks more deeply into some of the utility determinants of the pricing kernel, investigating in particular the effect of non-marketable background risks on the shape of the pricing kernel.-- Derives the prices of European-style contingent claims, in particular call options, in a one-period model; derives the Black-Scholes model assuming a lognormal distribution for the asset and a pricing kernel with constant elasticity, and emphasizes the idea of a risk-neutral valuation relationship between the price of a contingent claim on an asset and the underlying asset price.-- Extends the analysis to contingent claims on assets with non-lognormal distributions and considers the pricing of claims when risk-neutral valuation relationships do not exist.-- Expands the treatment of asset pricing to a multi-period economy, deriving prices in a rational expectations equilibrium.-- Uses the rational expectations framework to analyse the pricing of forward and futures contracts on assets and derivatives.-- Analyses the pricing of bonds given stochastic interest rates, and then uses this methodology to model the drift of forward rates, and as a special case the drift of the forward London Interbank Offer Rate in the LIBOR Market Model.

Lectures on Financial Mathematics

Greg Anderson,Alec N. Kercheval
Lectures on Financial Mathematics Book PDF

Author : Greg Anderson,Alec N. Kercheval
Publisher : Morgan & Claypool Publishers
Page : 51 pages
File Size : 48,9 Mb
Release : 2010
Category : Business & Economics
ISBN : 9781608454952

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Lectures on Financial Mathematics by Greg Anderson,Alec N. Kercheval Pdf

This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage," the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged to work through the exercises throughout the book. The intended audience is students and other readers who have an undergraduate background in mathematics, including exposure to linear algebra, some advanced calculus, and basic probability. The book has been used in earlier forms with students in the MS program in Financial Mathematics at Florida State University, and is a suitable text for students at that level. Students who seek a second look at these topics may also find this book useful. Table of Contents: Overture: Single-Period Models / The General Discrete Model / The Fundamental Theorems of Asset Pricing / Forwards and Futures / Incomplete Markets

Stochastic Finance

Hans Föllmer,Alexander Schied
Stochastic Finance Book PDF

Author : Hans Föllmer,Alexander Schied
Publisher : Walter de Gruyter
Page : 473 pages
File Size : 44,6 Mb
Release : 2008-12-19
Category : Mathematics
ISBN : 9783110212075

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Stochastic Finance by Hans Föllmer,Alexander Schied Pdf

This book is an introduction to financial mathematics. The first part of the book studies a simple one-period model which serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Such models are typically incomplete: They involve intrinsic risks which cannot be hedged away completely. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. In addition to many corrections and improvements, this second edition contains several new sections, including a systematic discussion of law-invariant risk measures and of the connections between American options, superhedging, and dynamic risk measures.

Continuous-Time Finance

Robert C. Merton
Continuous Time Finance Book PDF

Author : Robert C. Merton
Publisher : Wiley-Blackwell
Page : 754 pages
File Size : 46,5 Mb
Release : 1992-11-03
Category : Business & Economics
ISBN : 0631185089

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Continuous-Time Finance by Robert C. Merton Pdf

Robert C. Merton's widely-used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual finance choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance.

Introduction to Stochastic Calculus Applied to Finance, Second Edition

Damien Lamberton,Bernard Lapeyre
Introduction to Stochastic Calculus Applied to Finance Second Edition Book PDF

Author : Damien Lamberton,Bernard Lapeyre
Publisher : CRC Press
Page : 202 pages
File Size : 52,6 Mb
Release : 1996-06-01
Category : Mathematics
ISBN : 0412718006

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Introduction to Stochastic Calculus Applied to Finance, Second Edition by Damien Lamberton,Bernard Lapeyre Pdf

In recent years the growing importance of derivative products financial markets has increased financial institutions' demands for mathematical skills. This book introduces the mathematical methods of financial modeling with clear explanations of the most useful models. Introduction to Stochastic Calculus begins with an elementary presentation of discrete models, including the Cox-Ross-Rubenstein model. This book will be valued by derivatives trading, marketing, and research divisions of investment banks and other institutions, and also by graduate students and research academics in applied probability and finance theory.

Mathematics of Financial Markets

Robert J. Elliott,P. Ekkehard Kopp
Mathematics of Financial Markets Book PDF

Author : Robert J. Elliott,P. Ekkehard Kopp
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 54,9 Mb
Release : 2005
Category : Business & Economics
ISBN : 9780387212920

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Mathematics of Financial Markets by Robert J. Elliott,P. Ekkehard Kopp Pdf

This book presents the mathematics that underpins pricing models for derivative securities in modern financial markets, such as options, futures and swaps. This new edition adds substantial material from current areas of active research, such as coherent risk measures with applications to hedging, the arbitrage interval for incomplete discrete-time markets, and risk and return and sensitivity analysis for the Black-Scholes model.

Martingales and Financial Mathematics in Discrete Time

Benoîte de Saporta,Mounir Zili
Martingales and Financial Mathematics in Discrete Time Book PDF

Author : Benoîte de Saporta,Mounir Zili
Publisher : John Wiley & Sons
Page : 242 pages
File Size : 43,9 Mb
Release : 2022-01-26
Category : Mathematics
ISBN : 9781786306692

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Martingales and Financial Mathematics in Discrete Time by Benoîte de Saporta,Mounir Zili Pdf

This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time. The book offers a combination of mathematical teaching and numerous exercises for wide appeal. It is a useful reference for students at the master’s or doctoral level who are specializing in applied mathematics or finance as well as teachers, researchers in the field of economics or actuarial science, or professionals working in the various financial sectors. Martingales and Financial Mathematics in Discrete Time is also for anyone who may be interested in a rigorous and accessible mathematical construction of the tools and concepts used in financial mathematics, or in the application of the martingale theory in finance

Stochastic Finance

Hans Föllmer,Alexander Schied
Stochastic Finance Book PDF

Author : Hans Föllmer,Alexander Schied
Publisher : Walter de Gruyter GmbH & Co KG
Page : 608 pages
File Size : 54,7 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783110463453

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Stochastic Finance by Hans Föllmer,Alexander Schied Pdf

This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures

Continuous-Time Asset Pricing Theory

Robert A. Jarrow
Continuous Time Asset Pricing Theory Book PDF

Author : Robert A. Jarrow
Publisher : Springer Nature
Page : 470 pages
File Size : 45,6 Mb
Release : 2021-07-30
Category : Business & Economics
ISBN : 9783030744106

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Continuous-Time Asset Pricing Theory by Robert A. Jarrow Pdf

Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features ​new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.